A064491 - OEIS

%I #49 Dec 14 2021 02:06:12

%S 1,2,4,7,9,12,18,24,32,38,42,50,56,64,71,73,75,81,86,90,102,110,118,

%T 122,126,138,146,150,162,172,178,182,190,198,210,226,230,238,246,254,

%U 258,266,274,278,282,290,298,302,306,318,326,330,346,350,362,366,374

%N a(1) = 1, a(n+1) = a(n) + tau(a(n)), where tau(n) (A000005) is the number of divisors of n.

%C a(n) = partial sums of A165930(n). [_Jaroslav Krizek_, Sep 30 2009]

%D Claudia Spiro, Problem proposed at West Coast Number Theory Meeting, 1977. [If you change the starting term, does the resulting sequence always join this one? Does the parity of terms change infinitely often?] - From _N. J. A. Sloane_, Jan 11 2013

%H T. D. Noe, <a href="/A064491/b064491.txt">Table of n, a(n) for n=1..1000</a>

%F It seems likely that there exist constants c_1 and c_2 such that c_1*n*log(n) < a(n) < c_2*n*log(n) for all sufficiently large n. - _Franklin T. Adams-Watters_, Jun 25 2008

%F a(n+1) = A062249(a(n)). - _Reinhard Zumkeller_, Mar 29 2014

%t a[n_] := a[n] = a[n - 1] + DivisorSigma[0, a[n - 1]]; a[1] = 1; Table[a[n], {n, 1, 57}] (* _Jean-François Alcover_, Oct 11 2012 *)

%t NestList[#+DivisorSigma[0,#]&,1,60] (* _Harvey P. Dale_, Feb 05 2017 *)

%o (PARI) { for (n=1, 1000, if (n>1, a+=numdiv(a), a=1); write("b064491.txt", n, " ", a) ) } \\ _Harry J. Smith_, Sep 16 2009

%o (Haskell)

%o a064491 n = a064491_list !! (n-1)

%o a064491_list = iterate a062249 1  -- _Reinhard Zumkeller_, Mar 29 2014

%o (Python)

%o from itertools import islice

%o from sympy import divisor_count

%o def A064491gen(): # generator of terms

%o     n = 1

%o     yield n

%o     while True:

%o         n += divisor_count(n)

%o         yield n

%o A064491_list = list(islice(A064491gen(),20)) # _Chai Wah Wu_, Dec 13 2021

%Y Cf. A000005, A165930, A165494, A165495, A165496, A165497, A165498, A165499.

%K nice,nonn

%O 1,2

%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 04 2001

%E Beginning of sequence corrected by _T. D. Noe_, Sep 13 2007